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November 6th, 2017, 10:50 AM  #1 
Newbie Joined: Nov 2017 From: Latvia Posts: 2 Thanks: 0  I need help for a probability question
Let A, B be two events in a probability space. The probability that A happens is 1/2 The probability that B happens is 1/2 The probability that none of the events happen is 1/2 Compute the conditional probability P[A  B]. Are A and B independent? 
November 6th, 2017, 12:38 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,556 Thanks: 600 
If they were independent the probability of none happening is 1/4=(1P(A))(1P(B)), so they are not independent. P(A or B)=1P(none)=1/2 P(A or B)=P(A)+P(B)P(A and B) Therefore P(A and B)=1/2 leading to P(AB)=1. 

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